Problem: Simplify the following expression: $ n = \dfrac{x - 5}{-5x} + \dfrac{-10}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{x - 5}{-5x} \times \dfrac{7}{7} = \dfrac{7x - 35}{-35x} $ Multiply the second expression by $\dfrac{-5x}{-5x}$ $ \dfrac{-10}{7} \times \dfrac{-5x}{-5x} = \dfrac{50x}{-35x} $ Therefore $ n = \dfrac{7x - 35}{-35x} + \dfrac{50x}{-35x} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{7x - 35 + 50x}{-35x} $ $n = \dfrac{57x - 35}{-35x}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-57x + 35}{35x}$